Arrange ten cards numbered 1-10 in a pile. Turn over the top card,
then move the next card to the bottom of the pile. Turn over the new
top card and move the next card to the bottom of the pile. Continue
like this until all ten cards have been turned over. The challenge is
to arrange the pile so the cards are turned over in order from 1 to 10.

A piece of plywood has three holes it it: a circular hole with a
diameter of 2 cm, a square hole with 2 cm sides, and a triangular hole
with a base and height of 2 cm. What object could completely plug AND
pass completely through each hole?

A non-stop train leaves city A for city B at 60 m.p.h.... If to the
numerator and denominator of the fraction 1/3 you add its denominator...
A train moving at 45 m.p.h. meets and is passed by a train moving at 36
m.p.h...

A hardware plant makes rivets 6 inches long and 6 ounces in weight. Harry
makes a drum of rivets 6 inches long weighing only 5 ounces each. Harry's
drum is stored along with 9 other proper drums. Harry has to find the
rivets but he can only use a scale one time, and can take only one
reading from that scale. How can Harry be sure of picking the right drum
out of the ten?

A student struggles with a word problem that asks for specific sums of counting
numbers. Three different doctors weigh in with increasingly sophisticated and
comprehensive problem-solving approaches: programming spreadsheet formulas;
applying combinatorics; and invoking quadratic Diophantine and Pell equations.